please solve this problem
Answers
Answer:
Explanation :
\underline{\underline{\sf{\purple{Given\::-}}}}
Given:−
Two numbers are in ratio 4 : 5
Difference of their cubes = 61
\underline{\underline{\sf{\purple{To\:Find\::-}}}}
ToFind:−
Numbers = ?
\underline{\underline{\sf{\purple{Solution\::-}}}}
Solution:−
Here, we have ratio, i.e, 4 : 5 of two numbers and the difference of their cubes, i.e, 61 we have to find out both numbers. We will set up an equation by understanding the given conditions.
Let the numbers be 4n and 5n
Atq,
\qquad\longrightarrow\quad\sf (5n)^3 - (4n)^3 = 61⟶(5n)
3
−(4n)
3
=61
\qquad\longrightarrow\quad\sf 125n^3 - 64n^3 = 61⟶125n
3
−64n
3
=61
\qquad\longrightarrow\quad\sf 61n^3 = 61⟶61n
3
=61
\qquad\longrightarrow\quad\sf n^3 = \dfrac{61}{61}⟶n
3
=
61
61
\qquad\longrightarrow\quad\sf n^3 = \dfrac{\cancel{61}}{\cancel{61}}⟶n
3
=
61
61
\qquad\longrightarrow\quad\sf n^3 = 1⟶n
3
=1
\qquad\longrightarrow\quad\sf n = \sqrt[3]{1}⟶n=
3
1
\qquad\longrightarrow\quad\bf {n = \pink{1}}⟶n=1
Hence,
First number = 4n = 4 × 1 = 4
Second number = 5n = 5 × 1 = 5